The visual coupling between neighbors explains 'flocking' in human crowds

Patterns of collective motion or flocking in birds, fish schools, and human crowds are believed to emerge from local interactions between individuals. Most models of collective motion attribute these interactions to hypothetical rules or forces, often inspired by physical systems, and described from an overhead view. We develop a visual model of human flocking from an embedded view, based on optical variables that actually govern pedestrian interactions. Specifically, people control their walking speed and direction by canceling the average optical expansion and angular velocity of their neighbors, weighted by visual occlusion. We test the model by simulating data from experiments with virtual crowds and real human swarms. The visual model outperforms our previous overhead model and explains basic properties of physics-inspired models: repulsion forces reduce to canceling optical expansion, attraction forces to canceling optical contraction, and alignment to canceling the combination of expansion/contraction and angular velocity. Critically, the neighborhood of interaction follows from Euclids Law of perspective and the geometry of occlusion. We conclude that the local interactions underlying human flocking are a natural consequence of the laws of optics. Similar principles may apply to collective motion in other species.